The methods and apparatus of the present invention are especially suitable for monitoring and controlling the position, movement or velocity of an object driven by a non-rigid means, such as a belt, cable, or the like. An exemplary system that will be used for illustrative purposes throughout this disclosure is a shuttle carriage of an ink jet printer driven by a flexible cable, which is in turn moved by rotational motor drive output. Precise control is especially challenging where the mass is relatively large and the cable is, of necessity, flexible and somewhat elastic.
In printer applications, the desired shuttle carriage velocity profile is conveyed directly to a motor, and the motor generates rotational output corresponding to the desired velocity profile. A printer carriage is typically driven by a cable and pulley system or a cogged timing belt which translates the rotational motor drive output to printer carriage movement along a linear path. The timing belt or cable is flexible to accommodate the rotational motor drive output, and it is therefore subject to forces that cause the actual carriage velocity to deviate from the desired velocity profile. The flexible nature of the cable generates undesirable velocity ripples which cause print defects as a result of variations in ink drop exit velocity from the printer carriage. This problem is generally aggravated as the mass or object increases in weight and/or the cable increases in flexibility. In order to generate high fidelity images, such as during printing operations, the actual carriage velocity must be closely monitored and controlled to ensure that it corresponds as closely as possible to the desired velocity profile.
The cable or belt in the printer carriage system is equivalent to a linear spring that obeys Hooke's law, and deflection can therefore be determined as a function of the cable force. The cable or belt driven system is analogous to a mass/spring model system in which the internal damping in the cable is represented by a dashpot in parallel with the spring. In contrast to the more common case where one end of the spring is fixed, however, in the printer carriage mass/spring model system, the other end of the spring is not connected to mechanical ground. Instead, it is attached to the motor rotor, and the rotor is related to mechanical ground through an electromagnetic connection. Substantial deviation of the actual carriage motion from the desired velocity profile is due to extension or compression of the spring (belt or cable), and the remainder is due to errors in the position of the motor rotor.
In printer applications, at least two different control architectures have been implemented. According to one approach, an encoder or tachometer is mounted on the motor shaft to provide a motor shaft velocity signal. This system does not provide direct information concerning the position or velocity of the printer carriage, however, and it cannot correct for substantial deviation of carriage motion from the desired velocity profile due to forces exerted on the belt or cable. This approach therefore does not address a primary source of inaccuracy, since the printer carriage and the cable or belt are outside the servo loop.
A second control architecture employs a clock track encoder mounted on the carriage itself that reads a linear encoding strip mounted in fixed relationship to the carriage. According to this approach, the actual velocity of the printer carriage is monitored, but the responsiveness of the system can be unsatisfactory. In other words, the system is not effective in correcting deviations in the actual carriage position until the deviations have already occurred and printing errors have been introduced. This type of control system may thus be suitable for providing gross control functions, but it is limited in the fine control it can provide. Additionally, this control architecture presents a difficult servo system to implement because the resonant mass/spring system is in the loop.
One important principle of feedback systems design is that the servo system must not have a phase shift ("around" the loop) of 180.degree. or more for any frequency for which the system gain is unity or greater. If a higher phase shift is introduced, the servo system will oscillate rather than functioning as a linear feedback control system. In systems that incorporate a mass/spring system, it is easy to consume most of the 180.degree. allowable phase shift on the mass/spring portion of the system, leaving very little for the rest of the servo system. For this reason, it is difficult to incorporate mass/spring systems in servo loops.
To provide a stable servo loop in a single loop system incorporating a mass/spring component, it is generally necessary to reduce the system bandwidth and loop gain. In a velocity servo loop, loop gain is a good predictor of the velocity error which will result from a sudden increase or decrease of drag on the carriage. Similarly, the system bandwidth is indicative of the speed with which the servo can react to and recover from an adverse disturbance. Loop gain and bandwidth are therefore critical characteristics of the servo system, and high performance servo systems require elevated loop gain and bandwidth characteristics.